Question: The equation of a circle $C$ is $x^2+y^2+8y+15 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2) + (y^2+8y) = -15$ $(x^2) + (y^2+8y+16) = -15 + 0 + 16$ $x^2 + (y+4)^{2} = 1 = 1^2$ Thus, $(h, k) = (0, -4)$ and $r = 1$.